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<H2 class=postTitle><A 
href="http://codelines.net.au/uncategorized/genetic-algorithms-part-ii/">Using 
Genetic Algorithms To Solve Sudoku Puzzles - Part II</A></H2>
<DIV class=postMeta><SPAN class=date>Jun.02, 2006</SPAN> in <SPAN class=filed><A 
title="View all posts in Uncategorized" 
href="http://codelines.net.au/categories/uncategorized/" 
rel="category tag">Uncategorized</A></SPAN> </DIV>
<DIV class=postContent>
<P>See part I <A 
onclick="javascript:urchinTracker('/outbound/joshuahayes.blogspot.com/2006/05/genetic-algorithms-to-solve-sudoku.html');" 
href="http://joshuahayes.blogspot.com/2006/05/genetic-algorithms-to-solve-sudoku.html">here</A>.</P>
<P>Finally the end of another semester and another incredibly long week. It was 
a huge effort to get the software and report finished for AI in just over a 
week. Nevertheless, it was quite interesting. After running batch files, 
collating enourmous amounts of data, producing graphs and analysing algorithmic 
trends and points of interest it was all over. The final assessment in.After 
testing the canonical genetic algorithm (GA) we tested each of the additonal 
features we implemented; repair function, elites, random immigrants, adaptive 
mutation and the big kick. The latter was actually something I added at the last 
minute to make running tests a bit quicker from the batch file. After I realised 
it could potentially help with local maxima problems we were having I tweaked it 
a bit.Ted and I made many, many interesting observations from the data we 
collated.</P>
<P><A 
onclick="javascript:urchinTracker('/outbound/photos1.blogger.com/blogger/1917/2342/1600/immigrants.gif');" 
href="http://photos1.blogger.com/blogger/1917/2342/1600/immigrants.gif"><IMG 
alt="" src="" border=0></A>This graph is an example of introducing random 
immigrants back into the population. The slightly thicker red line represents 
the basic GA and is included to provide a baseline or normal. Here, you can see 
that the general trend of introducing immigrants into the population is that the 
population fitness is raised. Where the basic GA converged and was unable to 
find a solution, this feature helped.</P>
<P><A 
onclick="javascript:urchinTracker('/outbound/photos1.blogger.com/blogger/1917/2342/1600/basic.0.gif');" 
href="http://photos1.blogger.com/blogger/1917/2342/1600/basic.0.gif"><IMG alt="" 
src="" border=0></A>This charts shows the early convergence the basic GA 
exhibits on a tough problem.</P>
<P>&nbsp;</P>
<P><A 
onclick="javascript:urchinTracker('/outbound/photos1.blogger.com/blogger/1917/2342/1600/super.0.gif');" 
href="http://photos1.blogger.com/blogger/1917/2342/1600/super.0.gif"><IMG alt="" 
src="" border=0></A>This chart is an example of the Super GA (SGA) performance 
on the same problem as that above. The general fitness obtained for each 
population size of the Super GA is approx. 2-3 times greater then that of the 
basic GA. That is, the population fitness at convergence is considerably higher 
on the Super GA.This general trend of periods of stagnation then a rising of 
fitness is attributed to the big kick mentioned earlier. In some cases it forces 
the algorithm beyond the local maxima (observed just below fitness 90) allowing 
it to find the global maxima.</P>
<P><A 
onclick="javascript:urchinTracker('/outbound/photos1.blogger.com/blogger/1917/2342/1600/basicVsSuper.0.gif');" 
href="http://photos1.blogger.com/blogger/1917/2342/1600/basicVsSuper.0.gif"><IMG 
alt="" src="" border=0></A>This shows how our Super GA compared to our basic GA. 
It took quite a few generations and big kicks but the Super GA did eventually 
push beyond the local maxima to find the global maximum. Regardless of this, the 
overall fitness before convergence is higher. Thus, qualitatively the SGA does 
appear to be better.</P>
<P>These were but a few examples of the 30+ graphs we collated, each showing 
some new interesting trend. There were so many things we wished to explore but 
just did not have the time to do so. Our general consensus was that the 
canonical GA or SGA are not well suited to the Sudoku problem domain. A hybrid 
approach adopting a GA and some further metaheruistic like Tabu Search would 
prove to be an interesting study.Sorry about the poor quality, chopped up 
graphs. For some reason they just got totally garbled when copying them into 
Paint.Net. We didn’t really have time to optimise graph layout either. But it 
was an interesting study that I hope to continue further at some 
point.</P></DIV>
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